Question: Subtract $0.\overline{02}$ from 0.02 and express the result as a fraction.
Let's first convert $0.\overline{02}$ to a fraction. If we define the variable $s$ to be $0.\overline{02}$, then multiplying both sides of $s=0.\overline{02}$ by 100 gives us $100s = 2.\overline{02}$ Subtracting $s$ from $100s$ and $0.\overline{02}$ from $2.\overline{02}$ tells us that $99s = 2$ and thus $s=2/99$. We are asked to subtract 2/99 from $0.02 = 2/100$, which gives \[ \frac{2}{100} - \frac{2}{99} = \frac{2\cdot 99}{9900} - \frac{2\cdot 100}{9900}=\frac{198-200}{9900}= \frac{-2}{9900}= \boxed{-\frac{1}{4950}}. \]